00:01
You have f of x is x square root x plus 4.
00:12
What is the domain of the function? underneath the square root cannot be negative.
00:19
So the domain of the function, it can be negative 4 because then it would just be 0.
00:25
And it goes until infinity.
00:29
So that means x equals negative 4 becomes an important.
00:36
Critical point later.
00:40
Find the intervals where the function is increasing, where it's decreasing, find the x coordinates of the minima and the maxima.
00:50
Okay, perfect.
00:52
So we only need the first derivative to do that.
00:55
So the first derivative is the derivative of the, it's a product rule.
01:03
So the derivative of x times the square root of x plus four plus x.
01:09
And then times the derivative.
01:11
So 1 1⁄2, square root, not the square root, x plus 4 to the negative 1 half, and then the derivative of the inside is 1.
01:29
This reduces to 3x plus 8 over 2 times the square root of x plus 4...